Master Puzzler David Singmaster Delights in the Autobiography of Martin Gardner, Whose Scientific American Maths Column Enchanted Tens of Thousands

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he blames the crash of a Sukhoi Superjet in Russian society. He points to the number a good living standard comes from combin- 100 during a 2012 demonstration flight on of Russian scientists who remain psychologi- ing innovation in the real and digital econo- systemic failures rather than pilot error, sub- cally trapped in the Soviet tradition of keeping mies, and in services. But these demand clever sequently shown to be the cause. research separate from both enterprise and policies and frameworks, including a favour- Both Graham and Smil analyse human universities. Nevertheless, the next generation able climate for competition and investment, resources and education as sources of growth. is becoming aware that application and com- property protection and the rule of law. Smil reveals that the mercialization can complement fundamental Both the United States and Russia are traditional distinc- “No nation can scientific research and education. beginning to actively tackle their national tion between blue- survive solely Meanwhile, in the United States, willing- innovation challenges. The leap in the US and white-collar jobs on digital ness to take risks and convert inventions into chemical industry based on shale gas and is diminishing in the industry.” commercial propositions is falling off with the the modernization of the fuel sector and United States, push- rising standard of living, although it was once automotive industry in Russia seem to ing up the level of qualifications needed. And the norm, Smil shows. Population mobil- hold promise — but things may look very he shows that although US universities attract ity also enabled US innovation, he argues. different in the coming decade. Sustain- the best talent globally, the country’s overall Graham reveals this as another dissimilarity able growth in both countries will probably education system is failing to train enough to the situation in Russia, where even highly come from highly automated manufactur- qualified individuals. Some universities have educated citizens tend to “stay near where ing, which will demand a better educated thus been forced to give remedial courses in they were born”. But this is slowly changing: and trained labour force. The digitization subjects such as mathematics to first-year 37% of Moscow-based university students of manufacturing, encompassing robots, students. now hail from elsewhere in Russia or abroad. three-dimensional printing and more, will In Russia, Graham suggests, attempts to Approaches to growth, whether US or Rus- continue apace along with the need for new regenerate the research sector by attracting sian, can backfire. Smil points to the drive of skills. We will need, in short, to be ready for high-level scientists, upgrading equipment US businesses to maximize profits at short new twists in the road from lab to reality. ■ and making greater use of talented students notice and arrives at a provocative question: are providing the basis for innovation. The will the United States be able to maintain its Leonid Gokhberg is first vice-rector of first signs of high-tech entrepreneurship role as one of (if not the) leading economic the National Research University - Higher are appearing. A 2010 government direc- powerhouses by relying on digital-age busi- School of Economics (HSE) in Moscow and tive supporting university innovation has ness models? That question remains open. editor-in-chief of the journal Foresight- spawned multiple success stories, such as Taking Lonely Ideas and Made in the USA Russia. Dirk Meissner is deputy head of spin-off companies and growth in private- together, an overarching message emerges: the Laboratory for Science and Technology venture investment. Yet new initiatives, Gra- innovation needs to be allied to tangible out- Studies at HSE Institute for Statistical Studies ham argues, do not overcome the barriers comes, to something that people can use. No and Economics of Knowledge in Moscow. between science and innovation still inherent nation can survive solely on digital industry; e-mail: [email protected]

MATHEMATICS Master puzzler David Singmaster delights in the autobiography of Martin Gardner, whose Scientific American maths column enchanted tens of thousands.

or half a century, Martin Gardner Undiluted Hocus- eight, later following the famous US Tarbell (1914–2010) was an international Pocus: The Course in Magic. scientific treasure. As the author of Autobiography of Gardner hated high school, except for FScientific American’s Mathematical Games Martin Gardner mathematics and physics, noting that the column for 25 years, he introduced many MARTIN GARDNER (WITH “important history ... was the history of sci- PERSI DIACONIS AND thousands to the pleasures of mathemat- JAMES RANDI) ence”. Here, he writes, he penned “lots of ics. He enchanted tens of thousands more Princeton University Press: mediocre poetry” and invented ‘cherchez la with more than 100 books spanning eve- 2013. f e m m e’, a flexagon-type puzzle — flat paper rything from pseudoscience and magic to models folded different ways to reveal vari- Alice’s Adventures in Wonderland. To any- the Moon has phases, provided him with ous images. In 1934, when Gardner was just one who knows Gardner’s work, his self- a small laboratory and taught him some 20, Hobbies magazine published his article proclaimed “rambling autobiography” — the magic tricks. Gardner learned to read by on collecting mechanical puzzles — the first posthumously published Undiluted Hocus- looking over his mother’s shoulder as she of its kind. Pocus — comes as a delightful surprise. read aloud L. Frank Baum’s children’s clas- He had wanted to study physics, but Gardner reveals the roots of his unusual sic The Wonderful Wizard of Oz (1900). He instead read philosophy at the University mix of expertise in his childhood in Tulsa, subscribed to Science and Invention maga- of Chicago in Illinois. Its new president, Oklahoma. His father — a freelance oil zine and Amazing Stories, the first science- Robert Hutchins, fomented an educational prospector with a background in geology — fiction magazine, launched in 1926. He revolution by appointing Mortimer Adler taught Gardner basic science such as why performed his first magic trick at the age of to a chair in philosophy without consulting

and public-key cryptography, the basis of all financial transactions on the Internet. These pieces were eventually collected into 15 books. Magic gripped Gardner throughout his life, and he may have written more on it than ELLIOTT ERWITT/MAGNUM ELLIOTT on mathematics. I feel that his years spent writing for children may partly account for the exceptional clarity and direct- ness of his writing for adults. He became a leading expert on Lewis Carroll, with his Annotated Alice (Bramhall House, 1960) selling more than a million copies and explaining the mathematical, logical and literary associations in the book. He also became a specialist on Baum, the prolific British writer G. K. Chesterton, and some minor poets. Gardner produced so much, on so many subjects, that it was rumoured that his name was the pseudo- nym of a writers’ collective, such as the French mathematicians who published as Nicolas Bourbaki. DEBUNKING PSEUDOSCIENCE Gardner received an immense amount of correspondence and apparently replied to all of it. Many students, encouraged by his friendly and prompt replies, became mathematicians. Among scientists, Gardner is best known for his writing debunking pseudoscience. This began with ‘The Hermit Scientist’ in The Antioch Review of winter 1950–1951. In this, he described ideas such as psychia- trist Immanuel Velikovsky’s catastrophist theories about ancient history as exam- ples of pseudosciences created by persons working alone. He expanded these ideas in books such as Fads and Fallacies in the Name of Sci- ence (Dover Publications, 1957) and Science: Good, Bad and Bogus (Prometheus, 1981). In 1976, Gardner helped to found the Committee for Scientific Investiga- Martin Gardner, pictured in 1995. tion of Claims of the Paranormal (now the Committee for Skeptical Inquiry), which members of the department, most of whom Scripta Mathematica; these were gathered believes that it is “the duty of scientists to resigned. Hutchins and Adler went on to together for his first recreational mathemat- debunk bad science”. Amen. promote the Great Books scheme — a cur- ics book, Mathematics, Magic and Mystery, Gardner’s passion for writing and his riculum focused on texts by scientific and in 1956. warmth and humour shine forth on every literary luminaries from Archimedes to That same year, Gardner was shown page of this book, making it a mem- Virginia Woolf — and a highly flex- a hexahexaflexagon, a puzzle made by oir of a great human being — a ‘rational ible undergraduate programme. Gardner folding a length of paper into a hexago- man’, as Isaac Asimov had it. Almost all of enjoyed the ferment as philosophers came nal Möbius strip; it was the work of four Gardner’s books are still in print. They stand and went, and recalls seeing Enrico Fermi students at Princeton University (one of as a remarkable testament to the independ- cycling to the university’s Stagg Field, whom was Richard Feynman). Gardner ent scientific life. ■ where the great physicist was making the thought Scientific American might like an first atomic pile (an early reactor) in an article on it and the piece kick-started his David Singmaster is a retired professor underground squash court. much-loved column. In it, Gardner intro- of mathematics at London South Bank Gardner’s complex of interests began to duced or popularized a vast range of ideas, University and an honorary research fellow bear fruit in the 1950s, as he cut his writ- including polyominoes (the shapes formed at University College London. He was the ing teeth on journalism. He moved to New by joining squares edge-to-edge); the Soma first person to write about the Rubik’s Cube York to edit the quality children’s monthly cube; the superellipse; M. C. Escher’s iconic outside Hungary and devised the now Humpty Dumpty for eight years. He pub- images, such as the Endless Staircase; Roger standard notation for it. lished articles on maths and magic for Penrose’s tilings; and trapdoor ciphers e-mail: [email protected]